gradient.py

# cartesian product is 3^N
# all that have one or no zeros is 2^(N - 1) * (N + 2)
# all that have no zeros is 2^N
# all that have one zero is 2^(N - 1) * N
# index less than nonZero has no zeros, simple bitmask and shift to interpret bits as -1 or 1
# rest do that for N-1 fields then insert a zero

def gradient_helper(index, dimensions):
    result = []
    for i in range(0, dimensions):
        if index & 0x1:
            result.append(-1)
        else:
            result.append(1)

        index >>= 1

    return result

def gradient(index, dimensions):
    total = 2**(dimensions - 1) * (dimensions + 2)
    nonZero = 2**dimensions

    index = index % total
    if index < nonZero:
        return gradient_helper(index, dimensions)

    index = index - nonZero
    zeroAt = index % dimensions
    index = index / dimensions

    temp = gradient_helper(index, dimensions - 1)
    result = []
    i = 0
    j = 0
    while i < dimensions:
        if i == zeroAt:
            result.append(0)
            i += 1
            continue
        result.append(temp[j])
        i += 1
        j += 1

    return result